Characterizations of Hankel multipliers

TL;DR

This paper characterizes Hankel multipliers, especially radial Fourier multipliers, using Lebesgue space norms, and explores their boundedness, weak type inequalities, and interpolation properties.

Contribution

It provides new characterizations of Hankel multipliers in Lebesgue and Lorentz spaces, extending previous results to a broader class of multipliers.

Findings

Characterizations of radial Fourier multipliers in Lebesgue spaces.

Weak type inequalities for Hankel multipliers.

Interpolation results for multiplier spaces.

Abstract

We give characterizations of radial Fourier multipliers as acting on radial L^p-functions, 1<p<2d/(d+1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L^p-L^q bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces. Applications include results on interpolation of multiplier spaces.